In our piston pump, the displacement chamber above the piston head is sealed with an elastomeric sleeve, as a result of which the piston-shaped diaphragm is firmly connected to the cylinder unit at the open end. As the stroke movement of the piston adapts to the elastic expansion, there is no sealing gap. Via a lubricant layer, the elastomeric sleeve is supported against the cylinder wall and the conveying medium and lubricant do not come into contact with each other.