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Polymer Surface Design and Infomatics: Facile Microscopy/Image Analysis Techniques for Self-Organizing Microporous Polymer Film Characterization Simon D. Angus and Thomas P. Davis* Centre for Advanced Macromolecular Design, School of Chemical Engineering & Industrial Chemistry, The University of New South Wales, Sydney 2052, Australia Received May 29, 2002. In Final Form: September 19, 2002 Two methods are presented and exemplified for the characterization of self-organizing microporous polymer film surfaces via optical microscopy/image analysis. The first concerns the distribution of the pore diameters as measured by applying the Gini coefficient, which gives quantification to the degree of irregularity in this distribution while being sensitive to areas of regularity not necessarily present in the whole sample. The second technique, developed specifically for the purpose, quantified virtual light scattering (QVLS), concerns the difficult area of geometrical order in these films, assumed to be approaching hexagonally close-packed (HCP) in most instances. An algorithm is proposed that replicates the previous work of instrument-based light-scattering imaging but via a spatial infomatics analysis, therefore affording quantified parameters of the degree of order or otherwise present in the sample. QVLS is further exemplified by its application to a film-casting stage-temperature study and shows a favorable progression of geometry with stage-temperature reduction (range: 20-5 °C).

1. Introduction The pioneering observations of Franc¸ ois and co-workers,1 demonstrating that highly ordered thin films could be fabricated in a self-organizing manner2-4 without the aid of external templating,6-8 has sparked great interest in recent years. In our laboratories, the utilization of parallel developments in controlled radical polymerization (CRP)9,11 has extended the range of applicable materials to more complicated architectures such as star, block, and comb copolymers.9 The films produced by this technique stand in stark contrast to membranes that are currently commercially available (see Figure 1). Typically, these commercially available membranes are classified by their functional properties, and thus individual void diameters or geometrical ordering at the micrometer level are irrelevant. However, the films produced under “self-organizing” conditions show a propensity to form highly regular void diameters and ordered spatial geometry (see the example in Figure 2). The advent of this phenomenon has necessitated techniques of analysis that are specifically designed to discriminate between films in these highly ordered systems, techniques that were previously unnecessary as

Figure 1. Representative commercially available films: (a) Millipore HAWP, 0.45 µm, SEM 4 000×; (b) Sartorius SM 11 127, 0.2 µm, 5 000×.

* Corresponding author. E-mail: [email protected]. (1) Widawski, G.; Rawsio, M.; Francois, B. Nature (London) 1994, 369, 387. (2) See, for example, Gover, L.; Bashmakov, I.; Kiebooms, R.; Dyakonov, V.; Parisi, J. Adv. Mater. 2001, 13, 588. (3) Maruyama, N.; Karthaus, O.; Ijiro, K.; Shinomura, M.; Koito, T.; Nishimura, S.; Sawadaishi, T.; Nishi, N.; Tokura, S. Supramol. Sci. 1998, 5, 331-336. (4) Pitois, O.; Francois, B. Eur. Phys. J. B 1999, 8, 225-231. (5) Pitois, O.; Francois, B. Colloid Polym. Sci. 1999, 277, 574-578. (6) Templin, M.; Franck, A.; Du Chesne, A.; Leist, H.; Zhang, Y.; Ulrich, R.; Schadler, V.; Wiesner, U. Science (Washington, D.C.) 1997, 278, 1795. (7) Velev, O. V.; Jede, T. A.; Lobo, R. F.; Lenhoff, A. M. Nature (London) 1997, 389, 447. (8) Imhof, A.; Pine, D. J. Adv. Mater. 1998, 10, 697. (9) Stenzel-Rosenbaum, M.; Davis, T. P.; Chen, V.; Fane, A. G. J. Polym. Sci., Part A: Polym. Chem. 2001, 39, 2777-2783. (10) Stenzel-Rosenbaum, M.; Davis, T. P.; Chen, V.; Fane, A. G. Macromolecules 2001, 34, 5433-5438. (11) Matyjaszewski, K.; Miller, P. J.; Pyun, J.; Kickelbick, G.; Diamanti, S. Macromolecules 1999, 32, 6526-6535.

Figure 2. Inverted optical micrograph of self-organizing polymer film with HCP characteristics overlayed.

the images attest. Moreover, these films may be useful for the burgeoning needs of cell patterning and/or proteomics applications, and in these applications, the ability to locate and address each individual pore would enhance their usefulness enormously.

10.1021/la026006e CCC: $22.00 © 2002 American Chemical Society Published on Web 10/26/2002

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Figure 4. Schematic of ideal honeycomb pore (void) arrangement showing the position of the angle of alignment R and the PD characteristics.

Figure 3. Schematic of the infomatics scheme for selforganizing membrane technology.

Throughout the current literature and our own research, it has become apparent that small changes at the molecular level-achievable either by standard synthetic techniques such as end-group functionalization or modifications during CRP itself (e.g., degree of polymerization, copolymer ratio, arm number)-can have significant effects on both the ordering and pore diameter (PD) of the microporous films produced under standard conditions. Up to this point, however, only limited conclusions have been drawn with respect to these effects;12 quantitative study by Stenzel-Rosenbaum et al.13 focused solely on the change in PD achieved, with simple SEM interpretation used to ascertain pore-diameter estimates. Whereas other analytical surface techniques (including optical microscopy,4 laser-light scattering,14 and diffraction18) have been successfully applied to the films to elucidate aspects of the water vapor condensation process and droplet geometry progression, respectively, we are not aware of any studies that quantify the final film quality. From both an applied and mechanistic perspective, quantification of the film quality is of great importance, for without definitive correlations between film properties and corresponding casting conditions or molecular attributes of the casting solution, our understanding of either process will not advance. In addition to these understandings, if the enormous potential of these films is ever to be realized commercially, the ability to correlate casting conditions and molecular parameters with film quality in a numerical sense allows for the introduction of the increasingly embraced and powerful concept of infomatics in material design, that is, the coupled fabrication stages of (1) polymer chemistry and (2) casting conditions that lead to the final material could be successively informed by numerical characterization and infomatic databasing (Figure 3). It is possible that other authors have not considered film quality to be an important parameter, given that in our experience some initial variation of casting parameters eventually leads to a stepwise optimization of the films. However, it could also be that film micrographs previously (12) Francois, B.; Pitois, O. J. Adv. Mater. 1995, 7, 1041-1044. (13) Stenzel-Rosenbaum, M. H.; Davis, T. P.; Fane, A. G.; Chen, V. Angew. Chem. 2001, 40, 3428-3432. (14) Karthaus, O.; Maruyama, N.; Cieren, X.; Shimomura, M.; Hasegawa, H.; Hashimoto, T. Langmuir 2000, 16, 6071-6076. (15) Zenman, L.; Denault, L. J. Membrane Sci. 1992, 71, 221-231. (16) Zenman, L. J. Membr. Sci. 1992, 71, 233-246. (17) See, for a broad treatment, Ray, D. Development Economics; Princeton University Press: Princeton, NJ, 1998. (18) Srinivasarao, M.; Collings, D.; Philips, A.; Patel, S. Science (Washington, D.C.) 2001, 292, 79-83.

reported do not record true representative images since the casting process, particularly utilizing a direct air-flow setup as widely reported, can cause great intra- and interfilm quality variation. Whereas this approach may do well for purely investigative research into either the film-formation process or the range of materials that it applies to, any advance in understanding the mechanism at an experimental or even molecular level must draw its definitive conclusions elsewhere than occasional successes in an otherwise fickle procedure. 2. Approach Facile quantitative methods for determining final film surface quality were therefore developed in our laboratory to address this gap in the literature. Desirable attributes of such methods were (1) that they would give relatively fast feedback to the researcher in order that further casting or molecular changes could be quickly made and characterized and (2) that they are sensitive to small changes in the film quality (grain boundaries) in addition to identifying larger scale changes. It was also noted that whereas a “real-time” technique such as light scattering is desirable, the advantage of characterizing the final film is that the casting conditions can be changed almost without end since there is no requirement for complicated or bulky analytical instruments to be in the vicinity of the film-casting environment itself. Traditional techniques of surface imaging including AFM, confocal microscopy, or even SEM offer possible avenues for further work and are currently under investigation in our laboratories, but optical microscopy was first considered for its ease of use, relatively low cost, and negligible sample preparation. A combination of optical microscopy/digital imaging and software-based image analysis was employed to generate film surface data, which was then submitted to rigorous data analysis as follows. 2.1. Ideal Film. In determining incremental improvement such as quantified conceptions of “good” or “better”, one must define the ideal to be working toward. The ideal case is then defined as one where the voids appear closely packed in a hexagonal arrangement, with a 2-D lattice/ array quality as shown in Figure 4. Two helpful distinctions to be used with respect to the pore diameters are defined as follows: (1) Pore Size Regularity. A film displaying regularity of pore diameter would be one with a monodisperse (PD) distribution across all measurable voids; and (2) Pore Order. An ordered distribution of pores would be one where the voids fit into a 2-D hexagonal arrangement as shown in Figure 4, indicated, in its most ideal sense, by an appropriate angle of alignment (R) of 60°. Of course, it is to be noted that there is a possible interaction between the two qualities mentioned aboves it would be logical to assume that a regular distribution

Microporous Polymer Film Characterization

of pore diameters would provide the necessary conditions for the ordering of these voids into some 2-D arrangement. However, our experience in the laboratory would suggest that this connection does not always bear out, necessitating this distinction. 3. Experimental Section Polymer materials (five-“arm” star polystyrene, glucose initiated) used for film casting were initiated from R-D-glucose and 2-bromo-iso-butyrylbromide (98%, Aldrich) as described by Stenzel-Rosenbaum et al.10 via atom-transfer (radical) polymerization. Film casting was carried out dropwise on glass slides in a closed “shoe-box” construction casting house (relative humidity >80%) from solutions of polymer and solvent (100 mg mL-1, chloroform). Films prepared for Gini coefficient exemplification were cast at 20 °C whereas films used in the temperature study (exemplifying QVLS) were cast at ambient temperature, 20 °C, but with cooled-stage (metallic, digitally monitored) temperatures of 5, 10, 15, 17.5, and 20 °C. Further instrumental details are as follows: Size-Exclusion Chromatography (SEC). SEC analyses were performed on a modular system composed of a GBC LC1120 HPLC pump operating at room termperature, an in-line ERC3415 degasser unit, a SIL-10AD VP Shimadzu auto-injector with a stepwise injection-control motor with an accuracy of (1 µL, a column set that consisted of a PL 5.0-µm bead-size guard column and a set of 3- × 5.0-µm PL linear columns (103, 104, 105 Å) and an RI detector. Tetrahydrofuran was utilized as the continuous phase at a flow rate of 1 mL min-1 and a temperature of 40 °C. Polymer solutions were prepared with accurately known concentrations of 2.5 mg mL-1, whereas sample injection volumes of 50 µL were used. NMR Compositional Analysis. 1H NMR and 13C NMR spectra were recorded on a 300-MHz (Bruker ACF300) spectrometer using CDCl3 (Aldrich) as the solvent. Optical Microscopy. Film surface images were taken by reflectance microscopy on a coupled reflectance/transmittance optical microscope at various magnifications. A graticule was used to prepare scale bars for reference. Photos were captured with an onynx digital camera and recorded via PicoloDigiCAM digital imaging software. Image Analysis. Image analysis of digital photographs was carried out with Scion Image for Windows (Scion Corporation), release Beta 4.0.2, yielding pore-diameter data.

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G)

1

N N

∑ ∑ njnk|(yj - yk)| j)1 k)1

2n2µ

It sums the absolute differences between one value and all other values in a list of N data pairs (yj - yk) and then standardizes these differences for both the number of such differences (n2), the mean (µ), and for counting each difference twice. It can be seen that value of the coefficient will vary between 0 (in the case where the numerator is 0 or n ) ∞ and so gives the perfect equality case) and 1 (where the numerator is equal to the denominator, that is, perfect inequality). 4.1. Comparison with σ. To exemplify the inadequacy of a standard deviation (σ) calculation in identifying deviations from the ideal case, a population of N pores (mean ) µ) of which RN have PD A and (1 - R)N have PD B (where A > B) might be considered. Treating first σ, with a large N assumption, substitution yields the general result (eq 4.2)

σ ) xR(µ - A)2 + (1 - R)(µ - B)2

Whereas it is somewhat easy to distinguish between a regular distribution of PD and a nonregular distribution by visual inspection, subtleties of pore arrangement do not provide such ease of assessment. For example, what if the distribution is bimodal? Should the film characterization be “punished” for a second peak or “rewarded” for having an area of regular PD different from another area of regular PD (but a different modal PD from the first area)? It is our opinion that the film-casting process should recognize this regularity, regardless of whether it coincides with the PD mean or not. For in essence, a description of regularity should account for regular areas, whether they are across the whole film or not. Of course, the ideal case would be a perfectly regular film of one PD only, but at this stage, the casting process is liable to produce films that depart from this ideal, hence the requirement for a quantitative determination of this departure while recognizing regular regions. Turning to literature from other fields then, such a problem of pore-size distribution finds an analogous scenario in income distribution estimations.17 Instead of treating deviations from a mean point as stated above, it is useful to look at the differences between all data points (PDs). Such a measurement is the Gini coefficient (G) which encapsulates this aim well (eq 4.1):

(4.2)

Similarly, G can be calculated for this population as follows (eq 4.3):

G)

|(A - B)| 2N(R(A - B) + B)

(4.3)

It can be noted at this stage that with minimal assumptions (only that N is somewhat large) the general case of σ (eq 4.2) and G (eq 4.3) differ in that G encompasses N in the denominator whereas N has no effect on σ for the same case. The exemplification might be carried further by taking the extreme situation where the population is strictly bimodal (i.e., that R ) 0.5). With this measure, the two coefficients of variation reduce to

1 σ ) (A - B) 2

(4.4a)

|(A - B)| N(A + B)

(4.4b)

G) 4. Regularity

(4.1)

It is self-evident that with constant values of pore diameters A and B, the σ equation is blind to equal regions of regular pore diameter A or B and apportions the same degree of distribution whereas G, with an inverse N relationship, will reward larger sample numbers that display this bimodal (or trimodal or any number of ordered regions in the general case) by computing a lower G. 4.2. Application of G. The above method is demonstrated here by way of characterization of three films as shown in Figure 5. The films considered were all cast from chloroform (100 mg mL-1, RH > 80%) and used an R-D-glucose-pSTY star polymer material (Mw GPC = 4 000, 20 000, and 33 000 g mol-1). The data produced were converted to a standard frequency distribution plot (Figure 6). Now whereas it can be seen that there is a progression for the three different polymers from broadly dispersed pore diameters to narrowly dispersed pore diameters, as would be predicted by an inspection of the film images, actual quantified characterization is difficult with just the frequency distributions for the reasons mentioned above. By applying the G equation (eq 4.1) to the data, a clearer picture is developed (Table 1). It can now be seen that indeed the first of the films (a) performed poorly (G ) 0.23), with a relatively high

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Figure 7. (a) Typical scatter plot of ∆X vs ∆Y (unlimited) and (b) the same plot limited by eq 5.2 (note: only ∆X G 0 is plotted here).

Figure 5. Three films to be used in the pore-distribution survey.

Figure 6. PD frequency distributions captured via optical microscopy/digital image analysis. Table 1. Comparison of G and σ for the Three Films Shown in Figure 5 Mw GPC

G

σ

4 000 20 000 33 000

0.23 0.19 0.06

0.70 0.76 0.41

deviation from a regular distribution (Gtheoretical ) 0.00). Similarly, the second film (b), with its apparent bimodal distribution, has been rewarded for the areas of regularity with a lower G coefficienct (G ) 0.19). It is to be noted that the σ value reported here did not pick up on this improvement; rather, it recorded a worse (higher) value of σ ) 0.76 compared to the first film where σ ) 0.70. This is precisely as our previous proof work would attest. Not surprisingly, the final film (c) performed well on both indices, but with our knowledge of the powerful G computation, we can begin to make real comments as to the degree of “inequality” (irregularity) in this film as it approaches a G value of 0.00. 5. Order A somewhat more difficult computation is required to come at the question of the “ordered film”. After some

initial investigations that yielded interesting but ultimately unrewarding numerical correlations of ordered films to certain measurable parameters, our attention was turned back to previous instrument-based work, in particular, the successful application of light-scattering and laser diffraction experiments to these films by Pitois and Franc¸ ois5 and Karthaus et al.14 respectively. Here, they both show the real-time application of these techniques to the ordering of the film centers. Focusing then on the unique light-scattering properties of the hexagonal close-packed (HCP) arrangement of voids in a given “ideal” film, it was recognized that with the facile microscopy/digital imaging and image analysis techniques for collecting very specific pore-position data, a computational version of these instruments could be designed. 5.1. Quantified Virtual Light Scattering (QVLS). The image-analysis software was used to yield exact x - y positional data for the center of any n voids (n E 8 000, ∈I) in a given image. Subsequently, ∆X and ∆Y matrix pairs were found for the distances between each void and every other void in the sample (∆Y equivalent):

where

∆X vs ∆Y could then be plotted in a simple manner to yield the familiar instrumental light-scattering output (see Figure 7a and b). However, at this stage, whereas Figure 7a is obviously suggestive of ordered geometry given the evident clustering in the data, nothing more can be said of the original film than that which might have been concluded from the original imagesthat it is a “good” film.

Microporous Polymer Film Characterization

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Figure 8. Schematic of 1° neighbor positional characterization showing the position of rlim.

Therefore, further analysis drew directly upon comparison with an ideal arrangement. The data were first limited to only the 1° neighbor clusters since these will contain the most information about the geometry of the film (being the most predominant center-to-center distance). This was achieved by finding the total (pixel) area A of the sample image and calculating a void density, A/n, the area that each center ought to command in that image, given an equal distribution of such areas in the sample. Noting then that a center and its 1° nearest neighbors in a hexagonally close-packed arrangement would command seven such areas (see Figure 8), a circular area approximation was made, and a limiting radius (rlim) was calculated:

rlim )

x

7A πn

(5.2)

By applying this technique to the scatter plot in Figure 7, a limited 1° plot was made (Figure 7b). An initial order quantification can be made here, given that each center ought to fall on a single curve corresponding to the 1° center-center distance. This is achieved by computing the Pythagorean identity for each pair and computing the standard deviation (σ) from the mean: i,j)n R ) [ri,j]|i,j)1

where [ri,j] ) [x∆xi,i2 + ∆yi,i2]

and

Rlim ) {R|ri,j E rlim, i,j E n} σˆ (Rlim) )

σRlim µRlim

(5.3)

It is to be noted that a low σˆ (Rlim) value for the span of the 1° centers shows (only) adherence to the “halo” output of a standard scattering pattern. This indicates a replicated distance between each center and its nearest neighbor but says nothing about the particular geometry that the points might fall into. Further analysis ensued as follows. An algorithm to identify radial clustering of the data was developed. Again, assuming that the data would conform to the hexagonal close-packed arrangement, the clusters should form at points with a π/3 variation between them. However, to be more sensitive immediately to the clustering, a “scanning” region of π/6 was selected with a difference between each scan of π/18 to ensure that each cluster was characterized in full. The minimum (σˆ ) of such a set of scans was then taken to be the geometry characteristic of that film. The filtering algorithm is as follows: define:

X ˆ ) {∆xi,j|ri,j E rlim} Y ˆ ) {∆yi,j|ri,j E rlim} now

Θ(m) )

mπ Y ˆ π E tan ( ) E ( {(π3 - mπ 18 ) X ˆ 2 18 )} -1

and

σˆ (Θ) ) min{σ[Θ(m)]|1 E m E 15, m ∈I} (5.4a) 5.2. QVLS Exemplification (1)sThree Films. To show the power of the determination, three (real) films are considered, and both their σˆ (Rlim) and σˆ (Θ) characteristics are calculated by the method proposed (see Figure 9). Scatter plots of ∆X versus ∆Y were prepared as follows, clearly showing the different extents to which the replicated geometry is present in each (see Figure 10). The characterizations show this result well (see Table 2). As can be seen, whereas film b shows an improvement in σˆ (Rlim) relative to that in film c, it is only when the discriminator σˆ (Θ) is applied that the true geometry of film a shows through. In either case, the technique clearly distinguishes between the three films and gives very useful quantified information to the researcher. 5.3. QVLS Exemplification (2)sTemperature Effects of the Casting Environment. The method was further applied to a casting-stage temperature study. The same polymer as used in section 4 was used and applied

Figure 9. Three digital micrographs (phase-corrected for optimal image analysis characteristics) to be characterized by QVLS.

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Figure 11. σˆ (Θ) vs σˆ (Rlim). Progression from a disordered to halo to hexagonally close-packed (HCP) film structure is clearly evident at the different temperatures.

Figure 10. ∆X vs ∆Y for images a, b, and c in Figure 9 clearly showing regular HCP geometry (a), replicated distances or halo geometry (b), and random void position distributions (c). Table 2. Numerical Outcomes of the QVLS Method Applied to the Three Films in Figure 9 film

σˆ (Rlim)

σˆ (Θ)

a b c

0.0962 0.1974 0.3247

3.094 7.965 7.727

to a temperature-controlled ((1 °C) stage. Temperatures of 5, 10, 15, 17.5, and 20 °C were considered, and the resulting films were characterized as per the algorithms presented above. A useful plot was prepared (Figure 10) that shows the geometry progression that is created by decreasing the casting-stage temperature. Clearly, the more ordered films have both a low σˆ(Θ) and a low σˆ (Rlim), which is represented by the third quadrant of the plot. 6. Discussion The QVLS method produces almost identical visual outcomes to that of previous instrumental application in this area.5,14,18 The major difference, however, is that where this previous work provides for very good qualitative information by way of exposed photographic films, the microscopy/image analysis method presented here affords

the possibility of knowing exactly where each of these photons are “hitting” the page. It is from this strength that the QVLS method arises. Use of microscopy/image analysis in the characterization of membrane surfaces is not new; in fact, Zenman et al. showed the use of electron micrograph image analysis to provide good correlational information as to several properties of microfiltration membranes.15,16 They too note the benefits of the technique: it is noninvasive or destructive, relatively fast and cheap, provides accurate information on a range of morphological parameters, and can be extended to almost any physical correlation. It can be seen in the work above that the proposed methods well identify the geometric characteristics of the film under investigation. Naturally, their application is only for the film that approaches the ideal case as defined abovesa case of self-organizing macroporous films that is necessary only for very “high-end” applications such as templating and lithography. It is to be noted that as the Gini coefficient has come from economics and thus has a general application to any data, so too does the QVLS technique as mentioned above. That is, it will search for patterns in any kind of spatial data so long as appropriate assumptions about 1° neighbor positions can be made. As ever, however, one must be very careful when using numerical approaches to these problems. The assumptions involved and the machinery of the algorithms must be understood so that only appropriate conclusions are drawn. For example, in the above stage-temperature correlation work, the point in the fourth quadrant of the plot (enclosed in Figure 11) appears to have very good angle-based geometry (computing a low σˆ (Θ) but poor span-based geometry (computing a relatively high σˆ (Rlim)). One could conclude then that the sample consisted of voids whose centers fell neatly onto radial lines but were randomly spaced along those linessthis is inconceivable. Closer inspection of the sample image used, however, shows that there were gaps in the image where no voids existed at all, but the areas where there were void centers were shown to be in good geometric alignment. Here, the algorithm has over-estimated A/n and so used an rlim that instead of filtering out all void centers that lie outside the 1° neighbor position has included some of the 2° or even 3° neighbor clusters. It can be seen from this example that blind adherence to statistical or even analytical computations is rarely justified.

Microporous Polymer Film Characterization

The cooling of the casting stage and associated geometric benefits obviously speak to mechanistic considerations. It is not the purpose of this paper to enter into these here. However, the experiment shows the intended application of the above techniques and their ability to unlock vital information about these complicated systems and the paths that the film surfaces take to reach their final state. Significantly, whereas previous workers have in some cases controlled the plate temperature in a similar way,2,4 citing temperatures of 3-5 °C, we are not aware of any previous work that suggests that these conditions are necessary or optimal for the ordering of the polymer surface voids to occur. Indeed, these authors do not provide a reason for their selection of a cold stage, or in the case that one is given,4 it was to control surface evaporation for good optical microscopy imaging. Other authors have seemingly produced good films without controlling for stage temperature, maintaining the system at ambient conditions. However, whereas these previous findings show that the film-formation process may be somewhat “robust” for some polymer materials with respect to stage temperature, the study reported in this paper would suggest that the casting surface temperature is a major determinant of film-order formation for particular polymer materials,19 with cooler temperatures (10 °C) providing the most favorable conditions. We believe that such techniques fill the gap in the literature and should help to move the selforganizing membrane research work from being relatively fickle to being consistent and quantifiable. LA026006E