I CORRESPONDENCE Peak Shifts and Distortion Due to Solute Relaxation in Flow Field-Flow Fractionation Sir: The solute relaxation process in field-flow fractionation (FFF) may be defined as the phenomenon in which solute material far from equilibrium approaches its lateral equilibrium distribution in the FFF channel. The phenomenon is most important immediately after the solute sample is injected or carried into the fractionating channel. At this point, solute is invariably mixed over the entire flow cross section. Under the influence of the external field, however, it begins to accumulate (relax) into a narrow, exponential equilibrium layer next to one wall, termed here the accumulation wall (I, 2).
The time required for solute relaxation is potentially capable of creating important disturbances in normal FFF behavior. Solute that begins near the accumulation wall will reach equilibrium and, therefore, a state of normal retention almost immediately. However, solute entering the channel near the opposite wall must first cross the gap between the walls. Here it is subjected to the considerably higher velocity of flow in the center of the channel and is swept ahead of the solute already a t equilibrium near the accumulation wall. Thus the solute zone may be broadened and its center of gravity moved forward sufficiently at the very beginning to contribute substantially to an increased width and decreased retention volume of the final peak. A solution to this problem is the stop flow method (3-7) in which channel flow is halted as soon as the solute peak reaches the head of the channel. Relaxation occurs without the disturbing influence of differential velocity and thus flow is commenced again. The stop-flow method has proved effective in both thermal FFF ( 4 , 5 )and sedimentation FFF (6,7).However, at best it is an experimental inconvenience and at yrorst its interruption of flow creates baseline noise and instability. Therefore, it is preferable to avoid the stop-flow approach whenever possible. In order to do this, it is necessary to know the magnitude of the relaxation effect and the actual nature of the experimental disturbance. In this paper we will demonstrate experimental relaxation effects in a flow FFF system. The relaxation phenomenon, of course, occurs in virtually the same way for all FFF systems. Therefore, the results obtained here for flow FFF should be equally applicable to thermal, sedimentation, and electrical FFF.
THEORY The process of solute relaxation in FFF has been developed in some theoretical detail (I).The results, however, are expressed in the parameters of thermal FFF, not flow FFF. Below, we shall expand the conceptual basis of relaxation relative to the previous treatment, and present the most important theoretical results in a form suitable for application to flow FFF. Figure 1 illustrates the nature of the relaxation process. Individual particles (or molecules) are assumed to follow the relaxation trajectories. The trajectories are determined by the
combined action of axial flow and of lateral drift in the field. The angle of the trajectories varies according to the variable (usually parabolic) velocity from one point to another in the cross section. The trajectories are replotted from Ref. 1in a manner that shows the location and scale of the trajectories relative to the channel interior. The disturbances caused by diffusion have been ignored for simplicity. The zone finally deposited near the accumulation wall is bimodal. The two high concentration spikes are shown in the figure; these will be somewhat broadened by diffusion. Figure 1 shows the relationship between the width of the deposited zone, ho, and the channel length, L. The ratio, ho/L, depends on the relative mean velocity of axial flow and of drift in the field. In flow FFF, the drift velocity is simply the cross-flow velocity. In this system, h,/L is calculated more directly than in thermal FFF; it is simply the volumetric channel flow rate, V, divided by the volumetric cross-flowrate, VC
(ho/L)= V / V c
(1)
This is most easily verified by noting that when V = Vc,the channel flow and cross flow sweep out one channel volume in exactly the same time. The uppermost streamline of Figure 1will in that case reach the end of the channel ( z = L ) due to channel flow at the same time it reaches the bottom due to cross flow. Thus it intercepts the lower right hand corner, giving ho = L. This, combined with the fact that ho must be proportional to V, confirms the validity of Equation 1. Clearly, measurable peak shifts and band broadening can only be avoided when (ho/L)
