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Langmuir 2008, 24, 13030-13036
Entrance Effects at Nanopores of Nanocapsules Functionalized with Poly(ethylene glycol) and Their Flow through Nanochannels Raluca Popa,†,‡ M. Vraˆnceanu,†,‡ S. Nikolaus,† H. Nirschl,‡ and G. Leneweit*,† Carl GustaV Carus-Institute, Society for the Promotion of Cancer Therapy, Am Eichhof 30, 75223 ¨ schelbronn, Germany, and Institute of Mechanical Process Engineering and Mechanics and Niefern-O UniVersity of Karlsruhe, Strasse am Forum 8, 76131 Karlsruhe, Germany ReceiVed July 31, 2008. ReVised Manuscript ReceiVed September 18, 2008 We studied the effect of poly(ethylene glycol) (PEG) on the extrusion of large, multilamellar nanocapsules (also called liposomes or vesicles) through nanochannels with a length of 6 µm. For the generation of the nanocapsules, we used a lipid mixture with lecithin consisting of saturated and unsaturated fatty acids (dipalmitoylphosphatidylcholine (DPPC) and dioleoylphosphatidylcholine (DOPC)), cholesterol, and 2-8 mol % PEG linked to a lipid anchor (distearoylphosphatidylethanolamine (DSPE)) or the plain lipid anchor without PEG. An increase in PEG leads to a decrease of the critical tension for nanocapsule rupture (lysis tension) between 20-30%, whereas the pure lipid anchor does not produce any differences. We interpret these findings to be produced by a partial intrusion of the polymeric chain into the phospholipid bilayer of the nanocapsule which weakens its tensile strength. We evaluate statistically the discrepancies of lysis tensions found for different channels widths (50-100 nm) and two or four channels in series. Comparing our results on the flow resistance of either nanocapsules or pure water with lubrication theory, we find that the calculated viscous forces are not sufficient to account for the measured friction of nanocapsules. This shows that the nanocapsules are decelerated in the nanochannels by van der Waals interactions between channel and capsule walls and the intermediate water layer. The strength of these forces is 24 times higher for PEG and 94 times higher for the pure lipid anchor than the respective calculated viscous forces alone, showing that nanocapsule flow in nanochannels cannot be considered under the classical continuum assumption of the intermediate water layer.
1. Introduction Nanocapsules (which are often also called liposomes or vesicles) are quasi-spherical shells composed of lipid bilayers that encapsulate an aqueous space.1 The lipids are predominantly phospholipids, and in most cases the major component is phosphatidylcholine. The preparation often starts with multilamellar nanocapsules, which are then transformed into small unilamellar capsules using different techniques. A well-known, simple, and accurate method is the extrusion technique, which involves pushing the suspension of nanocapsules through pores of different diameters. Because of their physicochemical and biological characteristics, nanocapsules can be used in various applications: drug delivery vehicles in medicine, adjuvants in vaccination, signal enhancers/ carriers in medical diagnostics and analytical biochemistry, solubilizers and support matrix for various ingredients, and penetration enhancer in cosmetics.2 The aims of this study are threefold: first to characterize the entrance effect at nanopores of nanocapsules functionalized with poly(ethylene glycol) (PEG) chains, second to assess the comparability of these entrance effects for different pore sizes, and third to measure the flow resistance of either functionalized or nonfunctionalized nanocapsules in nanochannels. PEG is a hydrophilic nonionic polymer used in many biochemical and industrial applications. Due to its nontoxic character, it can be found in cosmetics, food, and pharmaceutical products.3 When * To whom correspondence should be addressed. E-mail: gero.leneweit@ carus-institut.de. Telephone: +49-7233-68443. Fax: +49-7233-68413. † Carl Gustav Carus-Institute. ‡ University of Karlsruhe.
(1) Frisken, B. J.; Asman, C.; Patty, P. J. Langmuir 2000, 16, 928–933. (2) Lasic, D. D. Liposomes: from physics to applications; Elsevier: Amsterdam, New York, 1993. (3) Annunziata, O.; Asherie, N.; Lomakin, A.; Pande, J.; Ogun, O.; Benedek, G. B. Proc. Nat. Acad. Sci. U.S.A. 2002, 99, 14165–14170.
PEG is attached to the surfaces of the nanocapsules, it is found to greatly increase the biological stability, reduce leakage of the encapsulated drugs, and permit major advances in therapeutic applications of liposomes.4 We focus on nanocapsules made of lipid mixtures of monounsaturated dioleoylphosphatidylcholine (DOPC), cholesterol, and saturated dipalmitoylphosphatidylcholine (DPPC), where DPPC is partially substituted by different amounts of PEG or its anchor lipid distearoylphosphatidylethanolamine (DSPE) for comparison. Lipid phase separation has been studied intensively recently.5-7 It was shown that ternary mixtures of DPPC, DOPC, and cholesterol form condensed complexes which can be visualized with fluorescence microscopy to separate from a second lipid phase, forming micrometer sized circular bright or dark “domains” on giant unilamellar vesicles.5,6 Evidence for phase separation is also given for nanocapsules consisting of dimyristoylphosphatidylcholine (DMPC) and cholesterol8 with liquid-ordered domains in the range of 20 nm. So far, no publication reveals the effect of PEG with its lipid anchor DSPE on the phase separation proofed for ternary mixtures and the tensile strength of such bilayers. As we only substituted 2-8 mol %, we assume no effect on domain formation, since fluorescent probes are frequently used at concentrations of 2 mol %. Our results show clear effects on both membrane tensile strength and flow resistance in nanochannels. The measurement (4) Tirosh, O.; Barenholz, Y.; Katzhendler, J.; Priev, A. Biophys. J. 1998, 74, 1371–1379. (5) Veatch, S. L.; Keller, S. L. Biophys. J. 2003, 85, 3074–3083. (6) Veatch, S. L.; Polozov, I. V.; Gawrisch, K.; Keller, S. L. Biophys. J. 2004, 86, 2910–2922. (7) Stottrup, B. L.; Stevens, D. S.; Keller, S. L. Biophys. J. 2005, 88, 269–276. (8) Loura, L. M. S.; Fedorov, A.; Prieto, M. Biophys. J. 2001, 80, 776–788.
10.1021/la8024777 CCC: $40.75 2008 American Chemical Society Published on Web 10/25/2008
Entrance Effects at Nanopores of Nanocapsules
of the relation of pressure drop versus flow rate during the extrusion of nanocapsules through membranes with well-defined pores, also called nanochannels, is well-established in the literature.1,9,10 The calculation of a so-called lysis tension where the nanocapsule forming bilayer disrupts above a certain minimum extrusion pressure is also confirmed by analytical theory and Monte Carlo simulation.11 However, there is no systematic study so far on the reproducibility of lysis tension for different lipid mixtures extruded through different pore sizes and evaluation of systematic errors produced by inaccuracies of the pores or nanochannels. Further, the flow resistance of deformed capsules through pores narrower than the undeformed capsule was studied by Bruinsma using lubrication theory.12 We will compare our results to his predictions to elucidate the questions of whether additional van der Waals interactions have to be taken into account besides the viscous forces used in his theory based on continuum mechanics. Our motivation to study the effect of PEG on nanocapsules with a specific ternary lipid mixture of DOPC/DPPC/cholesterol ) 20:50:30 mol % stems from a previous publication10 where we studied the mentioned lipids in different mixing ratios, some of them with lipid phase separation and some without. The lipid mixture chosen here shows phase separation,5,6 and nanocapsules of this mixture exhibited high values of both lysis tension and flow resistance, which is a necessary condition to check a possible effect on them produced by PEG when added to the lipid mixture.
2. Materials and Methods 2.1. Materials. The lipids 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-dipalmitoleoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[amino(polyethylene glycol)2000] (PEG2000-DSPE; with a molar weight of the polymer chain of 2000 Da), and 1,2-distearoyl-sn-glycero3-phosphoethanolamine (DSPE) were obtained partially as gift from Lipoid (Ludwigshafen, Germany), and cholesterol was from SigmaAldrich (Taufkirchen, Germany). All were received in powder form. As solvent, chloroform from Roth (Karlsruhe, Germany) was used. All materials had an estimated purity of more than 99% and were used without further purification. Bidistilled water with the quality for injectable drugs was used as buffer. 2.2. Sample Preparation and Extrusion. For the preparation of multilamellar nanocapsules, we used the film method. We first prepared stock solutions by dissolving the phospholipids in chloroform. Adequate quantities of the stock solutions were mixed and then exposed to vacuum for at least 30 min to remove the solvent on a rotary evaporator. After the solvent was removed, a thin and homogeneous film was obtained on the wall of a round-bottom flask. A few glass beads and water were added to the vessel and then agitated to suspend the lipid film. Multilamellar nanocapsules were spontaneously formed when water came in contact with the dried lipid film. The added water contained 0.5 mg/mL NaN3 to keep the nanocapsules microbiologically stable in time. The samples were used without pre-extrusion, and the stock suspension of nanocapsules was kept in the refrigerator and used within 5 days. Because the reliability of the experimental data depends on the sample quality, especially when the measurements are performed several days after sample preparation, we first performed experiments to get insight into the effects of aging on nanocapsule stability. The stability in time was monitored by extruding the sample after 0, 7, and 19 days of storage at +4 °C. Between days 0 and 7, we obtained reproducible results, but on day 19 we could observe changes in the increase of flow rate with pressure, that is, dQ/dp, and not in the minimum pressure pmin, which indicates changes of the sample constitution. (9) Hunter, D. G.; Frisken, B. J. Biophys. J. 1998, 74, 2996–3002. (10) Manojlovic, V.; Winkler, K.; Bunjes, V.; Neub, A.; Schubert, R.; Bugarski, B.; Leneweit, G. Colloids Surf., B 2008, 64, 284–296. (11) Gompper, G.; Kroll, D. M. Phys. ReV. E 1995, 52, 4198–4208. (12) Bruinsma, R. Phys. A 1996, 234, 249–270.
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Figure 1. Flow rate versus extrusion pressure of pure water and two samples of different lipid mixtures: (0) pure water; (4) DOPC/DPPC/ PEG2000-DSPE/Chol ) 20:42:8:30 mol %; and (O) DOPC/DPPC/ DSPE/Chol ) 20:42:8:30 mol %.
In a previous publication10 we checked sample stability and found that liposomes were stable for more than 12 days when stored at +4 °C. Before extrusion, the nanocapsule suspension was diluted with purified water to a concentration of 0.1 mg/mL lipids in water. This solution was extruded one time through two polycarbonate track etch membranes (PCTE membranes; Whatman, Maidstone, U.K.) in series with nominal pore diameters of 50, 80, and 100 nm. To see how the flow rate of liposomes is influenced by the length of the channels, we extruded not only through two membranes (2M) but also through four membranes (4M) of 100 nm. The extrusion was performed with a 10 mL extruder (Northern Lipids, Vancouver, Canada). The extrusion pressure was varied between 2 and 20 bar using pressurized argon. The pressure was measured with an electronic pressure sensor (WIKA Tronic, Klingenberg, Germany) with an accuracy of (0.01 bar and was registered with a video camera. The extrusion flow rate was measured using an electronic balance (Kern, Balingen, Germany) with an accuracy of (0.01 g, connected to a computer. The balance software records the weight every 2 s. A minimum of three weight values was registered (covering a minimum of 6 s) before the pressure was increased manually. From the weight values as a function of time, we calculated the flow rates and matched them with the pressure readings from the video sequence. The measurements were done at 20.0 ( 0.1 °C. In order to control the extrusion temperature, water from an external thermostat was circulated through the extruder. 2.3. Particle Size Analysis. The particle size was measured by photon correlation spectroscopy (PCS) using an N5 Submicron Particle Size Analyzer (Beckman Coulter, Miami, FL). A total of 50 µL of a 20 mM sample was put into a cuvette which was then filled up with buffer to 1.5 mL. The sample was equilibrated for 5 min at 20 °C in PCS. The measurement was started by working with three runs where each run consists of 10 single gaugings. Furthermore, the polydispersity index (PI) was determined.
3. Results and Discussion To study the influence of PEG on the extrusion of large, multilamellar nanocapsules through nanochannels, we used the following lipid mixture: DOPC/DPPC/cholesterol ) 20: 50:30 mol %. To observe the effect of the PEG chain, DPPC was partially substituted by 2, 4, 6, or 8 mol % of either PEG2000-DSPE or DSPE for comparison. As described in the Materials and Methods, we did not pre-extrude the raw liposomes, and all measurements were done on the first pass of the extrusion. Figure 1 shows the comparison of the linear curves for flow rate Q versus extrusion pressure p of water and two samples with
13032 Langmuir, Vol. 24, No. 22, 2008
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Table 1. Evaluation of the Measurements for pmin, (dQ/dp) According to eq 1, and Lysis Tensions γl According to eq 2; Further, the Coefficient of Correlation r2 in the Approximation of eq 1, the Number of Independent Experiments ne, the Total Number of Data Points nd, γl According to eq 2, and the Respective Standard Deviations s Are Shown lipids [mol %] PEG2000-DSPE
2
4
6
8
DSPE
2
4
6
8
pore diameter, 2Rp [nm]
no. of exp., ne
pmin ( s [×105 Pa]
jr2
γl ( s [mN/m]
no. of data points, nd
(dQ/dp ( s) [×10-6 m3/(s · Pa)]
100(2M) 80 (2M) 50 (2M) 100(4M) 100(2M) 80 (2M) 50 (2M) 100(4M) 100(2M) 80 (2M) 50 (2M) 100(4M) 100(2M) 80 (2M) 50 (2M) 100(4M)
8 4 2 5 6 4 2 4 4 4 4 4 5 4 3 4
6.20 ( 1.5 8.21 ( 0.7 6.53 ( 0.3 7.48 ( 0.8 6.01 ( 1.0 7.43 ( 0.8 7.16 ( 0.5 7.08 ( 0.51 4.94 ( 0.9 6.84 ( 1.3 5.91 ( 0.6 6.48 ( 0.9 4.89 ( 0.5 6.41 ( 0.8 5.51 ( 1.11 5.13 ( 0.3
0.981 0.981 0.989 0.981 0.977 0.993 0.992 0.987 0.973 0.975 0.951 0.988 0.981 0.978 0.987 0.995
15.5 ( 3.6 20.5 ( 1.8 16.3 ( 0.8 18.7 ( 1.9 15.0 ( 2.5 18.6 ( 2.0 17.9 ( 1.2 17.7 ( 1.3 12.4 ( 2.3 17.1 ( 3.2 14.8 ( 1.5 16.2 ( 2.2 12.2 ( 1.2 16.0 ( 1.9 13.8 ( 2.8 12.8 ( 0.7
38 28 12 40 29 27 19 37 19 19 28 27 28 29 22 27
8.4 ( 1.7 5.1 ( 1.0 2.9 ( 0.1 3.2 ( 0.4 9.0 ( 1.3 5.9 ( 0.6 3.6 ( 0.3 3.4 ( 0.3 8.7 ( 1.3 7.5 ( 2.1 3.3 ( 0.4 3.8 ( 0.4 6.5 ( 0.6 4.3 ( 0.2 2.2 ( 0.3 2.2 ( 0.1
100(2M) 80 (2M) 50 (2M) 100(4M) 100(2M) 80 (2M) 50 (2M) 100(4M) 100(2M) 80 (2M) 50 (2M) 100(4M) 100(2M) 80 (2M) 50 (2M) 100(4M)
3 3 3 4 5 3 2 4 5 3 3 5 5 5 6 4
4.50 ( 0.2 8.53 ( 1.4 8.85 ( 0.7 6.16 ( 1.3 5.69 ( 0.9 8.17 ( 0.7 9.092 ( 1.3 8.33 ( 2.6 6.15 ( 2.2 7.25 ( 1.8 10.16 ( 1.1 7.81 ( 1.4 5.45 ( 1.4 9.41 ( 0.9 10.26 ( 2.1 7.25 ( 0.8
0.990 0.981 0.976 0.945 0.978 0.978 0.955 0.983 0.987 0.970 0.975 0.965 0.981 0.979 0.977 0.962
11.3 ( 0.5 21.3 ( 3.5 22.1 ( 1.8 15.4 ( 3.1 14.2 ( 2.3 20.4 ( 1.8 22.7 ( 3.2 20.8 ( 6.6 15.4 ( 5.6 18.7 ( 4.9 25.4 ( 2.8 19.5 ( 3.4 13.6 ( 3.5 23.5 ( 2.3 25.7 ( 6.0 18.1 ( 1.9
17 15 18 26 28 17 12 23 26 19 20 29 31 22 30 21
3.2 ( 0.1 2.3 ( 0.4 1.5 ( 0.1 1.1 ( 0.1 3.9 ( 0.4 2.4 ( 0.3 1.6 ( 0.1 2.1 ( 0.3 4.0 ( 1.0 2.1 ( 0.2 1.9 ( 0.1 1.5 ( 0.1 3.5 ( 0.7 2.1 ( 0.4 1.8 ( 0.3 1.3 ( 0.1
8 mol % of either PEG2000-DSPE or pure DSPE. At very low pressures, nanocapsules remain unextruded on the membrane, resulting in creeping flow of pure water. Therefore, previous authors established a method to obtain the minimum pressure needed for the rupture of big, multilamellar nanocapsules by extrapolation of the linear relation of pressure versus flow rate to vanishing flow rate1,9,10 as shown in Figure 1. The pressure value extrapolated for Q ) 0 represents the minimum extrusion pressure pmin. In the range of pressures p and flow rates Q shown in Figure 1, their relationship is approximated to first order by
Q(p) )
(p - p ( dQ dp )
min)
the coefficients of correlations of all linear regressions jr2 is shown (column 6). Table 1 contains all data produced by the measurements which will be evaluated in the following in graphical form and using statistical methods. We will first focus on the question how the PEG concentration influences the lysis tension γl (and propor-
(1)
Although the linearity of each test run is fairly good, as can be seen from the linear regressions and the respective data points in Figure 1, these regressions are not ideally reproducible. Instead, they scatter, producing different pmin and dQ/dp values for each test run. To deal appropriately with these statistical fluctuations, we decided to average without discarding any measurement to avoid any bias. In Table 1, we specify the total number of reproducing experiments with identical sample/ membrane combinations (column 4). The number of experiments is between two and eight, where only fresh membranes were employed for each experiment for a 10 mL sample. Table 1 also shows the total number of measured data points (column 8), which is between 12 and 40. On average, five to six data points were collected in each experiment. From each experiment, a linear regression according to eq 1 was performed, yielding pmin and dQ/dp which were averaged and displayed with their respective standard deviations s in Table 1. Also, the average of
Figure 2. Lysis tension γl of PEG2000-DSPE at different concentrations and different pore diameters: (]) 100 nm (2M); (0) 80 nm (2M); (4) 50 nm (2M); and ([) 100 nm (4M). To avoid an overlap of error bars (only shown for either + or -), data points are displayed staggered along the abscissa by (0.2 mol %; the real PEG2000-DSPE content was 2.0, 4.0, 6.0, and 8.0 mol % in all cases (please note that the ordinate scales from 10 to 24 and not from 0-24).
Entrance Effects at Nanopores of Nanocapsules
Langmuir, Vol. 24, No. 22, 2008 13033
Figure 3. (a) Geometry of a deformed nanocapsule in a nanochannnel with the lubricating gap h being determined by lubrication theory (see eq 4) and the gap length L by equating the surface of the deformed nanocapsule with that of an undeformed one (see Table 4). (b) Illustration of a nanocapsule with a polymer chain in a nanochannel. (c) Scanning probe electron microscopy image of a polycarbonate track etch membrane (scale bar, 1 µm; double holes are marked by white circles). Table 2. Evaluation of a Possible Dependence of γl and dQ/dp of Samples on the Concentration of Either PEG2000-DSPE or DSPE Using Student’s t-test, eq 2, Also Showing the Linear Correlation Function γl(xz) ) γl,0 ( (dγl/dxz)xz (with xz ) xPEG or xDSPE), Its Coefficient of Correlation r2, the Error Probability P for the Assumed Correlation, and the Number nd of Independent Data Points lipids
pore diameter, 2Rp [nm]
PEG2000-DSPE
100 80 50 100(4M) 100 80 50 100(4M)
DSPE
γl [mN/m] 16.92 21.81 18.51 21.03 11.81 16.17 20.86 16.76
- 0.62xPEG - 0.75xPEG - 0.54xPEG -0.94xPEG + 0.42xDSPE + 0.82xDSPE + 0.62xDSPE + 0.35xDSPE
tionally the minimum extrusion pressure pmin) of the nanocapsules. Figure 2 shows how increasing the content of PEG2000DSPE from 2 to 8 mol % decreases the lysis tension between 21 and 31% at constant pore size. We can explain this if we take into consideration the fact that PEG grafted onto a nanocapsule may exist in either the “mushroom” or the “brush” regime.13 In the mushroom regime, the PEG configuration is similar to that of a single chain in solution coiled approximately spherically due to the absence of lateral interactions with neighboring chains. Its approximate size is characterized by the Flory dimension Rf, with Rf ) 3.66 nm for PEG2000.14 The mushroom regime of PEG2000-DSPE is in the range 0 < xPEG < 4 mol %. At higher grafting densities, that is, xPEG > 4 mol %, the chains interact laterally, which implies distances D between PEG lipids anchored at the nanocapsules surface which are smaller than the polymer coil, that is, D < Rf. The latter is called the brush regime. In this regime, the polymer coil is deformed with an extension length LPEG from the bilayer surface to the free chain end. From ref 15, we deduced that the extension length LPEG of the PEG chain from the bilayer surface is LPEG 3.7, 4.3, 5.0, and 5.7 nm for xPEG ) 2, 4, 6, and 8 mol %, respectively. Thus, the extension length LPEG is of the same order as the thickness of the lipid bilayer forming the shell of the nanocapsule, which is between 3.6 and 4.6 nm for different lipid mixtures, measured as peak-peak headgroup distance with X-ray diffraction.16 As shown in Figure 2, the lysis tension decreases with increasing concentration of PEG, and with an increasing extension length LPEG of the PEG chains from the bilayer surface. In principle, the lysis tension should be independent of the pore size. However, the averaged values of different pore (13) deGennes, P. G. AdV. Colloid Interface Sci. 1987, 27, 189–209. (14) Kenworthy, A. K.; Hristova, K.; Needham, D.; McIntosh, T. J. Biophys. J. 1995, 68, 1921–1936. (15) Needham, D.; Zhelev, D. V.; McIntosh, T. J. In Liposomes: Rational Design; Janoff, A. S., Ed.; Marcel Dekker: New York, 1999; Chapter 2, pp 13-62. (16) Rawicz, W.; Smith, B. A.; McIntosh, T. J.; Simon, S. A.; Evans, E. Biophys. J. 2008, 94, 4725–4736.
r2
P [%]
nd
(dQ/dp ( s) [×10-6 m3/(s · Pa)]
r2
P [%]
0.086 0.415 0.321 0.649 0.058 0.222 0.124 0.036
>10 5 10 >5 >10 >10
23 16 11 17 18 14 14 17
8.17 ( 1.13 5.65 ( 1.25 3.00 ( 0.59 3.18 ( 0.65 3.95 ( 0.73 2.32 ( 0.07 1.67 ( 0.21 1.35 ( 0.28
0.169 0.005 0.216 0.186 0.005 0.038 0.066 0.004
>5 >10 >10 >5 >10 >10 >10 >10
sizes scatter by 19-28% at equal PEG2000-DSPE concentration. However, when we take into account the error bars, we find that no statistically significant deviation for the same sample occurs between the values for 100 nm (4M) and all others, except for the data points with 80 nm and 8 mol % PEG2000-DSPE. As can be seen in Figure 2, the values of the samples extruded through 50; 80; and 100 nm (4M) coincide within an interval of (10%. Only the values for extrusion through 100 nm (2M) deviates more. What could be the physical reasons for the discrepancies of γl measured at different pore sizes and its fluctuations? When we compare lysis tensions calculated for extrusions through different pore sizes, we have to take into account possible deviations between the nominal and the real averaged pore radius in the range of (10%, but this possible source of inaccuracy could only explain the discrepancy between 50; 80; and 100 nm (4M). However, an assumed deviation between nominal and real pore radius would not explain the discrepancy of γl between measurements with 100 nm pores with either (2M) or (4M). This discrepancy is most likely caused by “double holes”, that is, the merging of two pores, since γl is larger for (4M) than for (2M), which indicates that the effective pore size might be underestimated in the case of (2M). Double holes, which can be seen in Figure 3c inside the white circles, are defects of the membranes. The effects of these defects can be minimized by increasing the number of the membranes. The probability that nanocapsules extruded through a double hole of the first membrane would flow through double holes of the next membranes without being extruded through holes of regular size decreases exponentially with the number of membranes used in series. Therefore, double holes are the most probable explanation for the discrepancies of γl and its standard deviation shown in Figure 2. Using Student’s t-test, we calculated and compared the increase of the flow rate Q with increasing pressure, that is, dQ/dp, and the lysis tension γl of the two different classes of samples. The t-test uses a distribution function tP,m that is given by17 (17) Bronstein, I. N.; Semendjajew, K. A. Taschenbuch der Mathematik; Nauka: Moscow, 1991.
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Table 3. Comparison of the Values of dQ/dp and γl of Samples with Either PEG2000-DSPE or DSPE Using Student’s t-Test, eq 3 pore diameter, 2Rp [nm]
(dQ/dp ( s)PEG [×10-6 m3/(s · Pa)]
ne,PEG
(dQ/dp ( s)DSPE [×10-6 m3/(s · Pa)]
ne,DSPE
T
k
P [%]
(dQ/dpPEG)/ (dQ/(dpDSPE)
100(2M) 80 (2M) 50 (2M) 100(4M)
8.17 ( 1.13 5.65 ( 1.25 3.00 ( 0.59 3.18 ( 0.65
23 16 11 17
3.95 ( 0.73 2.32 ( 0.07 1.67 ( 0.21 1.35 ( 0.28
18 14 14 17
14.10 10.25 8.21 9.75
39 28 23 32
10 5% in all cases). Therefore, we only show averages of dQ/dp ((s) in Table 2 and no regressions to linear functions. However, there is a big difference of the respective flow resistances when comparing the results with either PEG or DPSE at equal pore size. In Table 3, the averages of dQ/dp for all xPEG (column 2) and xDSPE (column 4) are shown. The last column of Table 3 shows the ratio (dQ/dp)PEG/(dQ/dp)DSPE. As can be seen, the increase in flow rate with pressure is between 1.88 and 2.43 times higher for samples with PEG compared to those without PEG (see column 9 in Table 3). This difference is highly significant for all Rp (P < 0.1%). In comparison, the difference in flow resistance between pure water and PEG is only 22%, that is, ((dQ/dp)H2O/ (dQ/dp)PEG) ) 1.22. In Table 4, we compare our results on the flow resistance of nanocapsules with the theoretical results by Bruinsma,12 who used lubrication theory to calculate the permeability K of deformable capsules in infinite tubes:
Q)K
πRp2 ∆p η ∆l
with
(
K ) Rp2 8 + 0.233nNC and
L3 Rp2
)
-1
( )
h ≈ 2.05Rp
ηQ πRp2γ
2 3
(4)
Here, η is the dynamic viscosity, ∆p/∆l is the pressure drop per unit pore length, L is the length of the cylindrical shaft of the deformed nanocapsule as shown in the geometrical sketch in Figure 3a, h is the width of the lubrication gap, and γ is the tension between the frontal and rear end cap of the deformed nanocapsule. PCS measurements of the sizes of the samples extruded through 80 nm (2M) show slight size differences between samples with either PEG or DSPE but no influence of the amount of these compounds (either 2 or 8 mol %) on the sizes. The polydispersity indexes ensure that all samples can be assumed to be monodisperse. Using the measured radii of the nanocapsules RNC, we calculated the lubrication gap h, the length L of the lubrication zone, and the permeability K and display them in Table 4. L was determined by equating the surface of the spherocylinder of the deformed nanocapsule with the surface of a sphere of radius RNC. This is justified by the fact that phospholipid bilayers can only be expanded by maximally 3-5% before rupturing.18 K was calculated assuming one nanocapsule per pore of 6 µm length, which is much higher than the volumetric average of nanocapsules per pore nNC (see last column in Table 4). The gap h is strongly influenced by the bilayer tension γ. Bruinsma12 assumes values γ ) 0.5-1.0 mN/ m, but our results show that γl is much higher. Using γl for the calculation of h (column 5 in Table 4), the values of h are of the order of 1 nm, which would mean that the gap is virtually free of water since the intermolecular distance between two water molecules is about 0.4 nm. Therefore, we also calculated h, L, and K assuming γ ) 0.5 mN/m (see columns 8-10 in Table 4). In the latter case, h ≈ 10 nm, which appears physically more realistic concerning the interstitial water layer. Since there is no size difference for either 2 or 8 mol % of the same compound, K is also practically constant and can be averaged. When we compare KPEG/KDSPE ) 1.02 (γ ) γl) or 1.03 (γ ) 0.5 mN/m) with the measured flow resistance
((dQ/dp)PEG /(dQ/dp)DSPE) ) 2.43, KH2O/KPEG ) 1.04 (γ ) γl), or 1.14 (γ ) 0.5 mN/m) with ((dQ/dp)H2O/(dQ/dp)PEG) ) 1.22, we realize that even for an assumed number of one nanocapsule per pore the friction effect calculated with lubrication theory does not suffice to account for the measured resistance of the nanocapsules. Here, we see that the choice of γ in the calculation of h influences K only moderately. However, in addition, we have to consider that there are far less nanocapsules per pore for the given lipid concentration of 0.1 mg/mL: the volumetric average of nNC shows that only about 0.7% of all pores would be filled, and in this case the permeabilities K are practically equal, thus KH2O = KPEG = KDSPE. Therefore, additional friction forces must be acting besides viscosity, which is the only force taken into account by lubrication theory. The estimated gap width h ≈ 1-10 nm would be in the transition range of continuum and molecular mechanics. Therefore, two types of van der Waals interactions have to be considered: first an interaction between the lubricating water layer and both enclosing solid walls, and second an interaction between the nanocapsule and the pore walls. For the first type of interaction, Forcada and Mate19 show that lubricating films of 4-10 nm thickness produced by spin coating show an increase of their apparent viscosity of 50-80% compared to the viscosity of the same fluid when it flows in a truly continuum mechanical geometry. For an explanation of the measured friction, we propose that the nanocapsules are strongly decelerated in the pores owing to van der Waals attraction, so that not only the theoretically assumed 0.7% of all pores are filled with one nanocapsule but in fact 18.3% for PEG and 66.4% for DSPE. This is only possible when the nanocapsules are strongly decelerated so that they stay much longer in the pores than predicted by Bruinsma.12 We interpret this deceleration to be caused by the combined action of two types of van der Waals attraction mentioned. Quantitatively, their deceleration effect is about 24 (PEG) or 94 (DSPE) times stronger than that of the viscous forces in the lubrication film assuming a viscous force in the frame of continuum mechanics. Our physical interpretation of this quantification and the difference in flow resistance between nanocapsules with PEG and those without is that the PEG chains and their surrounding hydration layer largely shield van Waals attractions occurring between the lipid bilayer and the polycarbonate pore wall.
4. Conclusions We studied the influence of PEG on the extrusion of large multilamellar nanocapsules. We find that when PEG is attached to the surface of nanocapsules, it influences the lysis tension γl and the minimum extrusion pressure pmin. For all the samples with PEG, the lysis tension decreases between 20 and 30% with increasing PEG concentration, whereas no significant change is observed when PEG is substituted by different amounts of DSPE. We interpret these findings with a partial intrusion of the polymeric chain into the phospholipid bilayer of the nanocapsule which weakens its tensile strength. The lysis tension should be independent of the pore sizes, which is indeed the case when a sufficient number of the membranes are used: Using four membranes in series, no significant deviations compared to all other measurements were found. Inaccuracies in the measurements are attributed to double holes, that is, defects of the nanochannels, (18) Needham, D.; Nunn, R. S. Biophys. J. 1990, 58, 997–1009. (19) Forcada, M. L.; Mate, C. M. J. Colloid Interface Sci. 1993, 160, 218–225.
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which can be minimized with a higher number of membranes but which necessitate evaluation of all findings statistically. The substitution of PEG by DSPE helps to illuminate the influence of the polymeric chain. The increase of flow rate with pressure dQ/dp is independent of the amount of either PEG or DSPE but is significantly different for these two classes of samples (p < 0.1%). Comparing our results on the flow resistance of nanocapsules and pure water with lubrication theory, we find that viscosity as it is defined for a macroscopic system is not sufficient to account for the measured friction. This shows that the nanocapsules in the pores are decelerated by van der Waals interactions between pore and capsule walls
Popa et al.
and the intermediate water layer, which is about 1-10 nm in width. The strength of these van der Waals forces is about 24 times higher in the case of PEG and 94 times higher for DSPE than the flow resistance of viscosity in a macroscopic system, showing that the forces encountered are outside the frame of classical continuum mechanics. Acknowledgment. We gratefully acknowledge funding provided by the Deutsche Forschungsgemeinschaft (DFG), Le 1119/ 4-1 and by the German Ministry of Education and Research (BMBF) in the frame program “Microsystems”, KARMI-KF, 16SV3569. LA8024777
